Clavius, Christoph, Geometria practica

Table of figures

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          <pb o="97" file="127" n="127" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s3686" xml:space="preserve">
              <emph style="sc">Si</emph>
            autem dioptra per C, tranſierit, erit
              <lb/>
            altitudo A E, diſtantiæ quęſitæ E H, æqua-
              <lb/>
              <figure xlink:label="fig-127-01" xlink:href="fig-127-01a" number="55">
                <image file="127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/127-01"/>
              </figure>
            lis: </s>
            <s xml:id="echoid-s3687" xml:space="preserve"> cum ſit vt AD, ad DC, æqualem,
              <note symbol="a" position="right" xlink:label="note-127-01" xlink:href="note-127-01a" xml:space="preserve">4. ſexti.</note>
            A E, ad EH.</s>
            <s xml:id="echoid-s3688" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3689" xml:space="preserve">
              <emph style="sc">Si</emph>
            denique vmbra abſciſſa fuerit ver-
              <lb/>
            ſa, vt BK, erit altitudo AE, minor, quam
              <lb/>
            diſtantia E F, quod plerunq; </s>
            <s xml:id="echoid-s3690" xml:space="preserve">in diſtantiis
              <lb/>
            w
              <unsure/>
            etiendis accidere ſolet; </s>
            <s xml:id="echoid-s3691" xml:space="preserve">eritq; </s>
            <s xml:id="echoid-s3692" xml:space="preserve">triangu-
              <lb/>
            lum ABK, triangulo AEF, æquiangulum,
              <lb/>
            cum anguli B, E, recti ſint, & </s>
            <s xml:id="echoid-s3693" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-127-02" xlink:href="note-127-02a" xml:space="preserve">29. primi.</note>
            BAK, AFE, æquales. </s>
            <s xml:id="echoid-s3694" xml:space="preserve"> Quare ſi fiat,</s>
          </p>
          <note symbol="c" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt part{es} vmbræ \\ verſæ BK, # ad lat{us} quadrati \\ AB, 1000. # Ita altitudo no- \\ ta AE, # ad E F, diſtan- \\ tiam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3695" xml:space="preserve">producetur quæſita diſtantia EF, in partibus altitudinis erectæ AE.</s>
            <s xml:id="echoid-s3696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3697" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3698" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            diſtantia non valdè magna eſt, vel extremum eius punctum
              <lb/>
            facilè videri poteſt ſatis erit, ſi qua dratum ſupra planum Horizontis con-
              <lb/>
            ſtituatur, ita vt vmbrę verſę latus B C, ad punctum illud recta vergat. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">Vt ſi di-
              <lb/>
            ſtantia horizontalis D M, metienda ſit, eique imponatur Quadratum erectum,
              <lb/>
            mouenda eſt dioptra, donec linea fiduciæ in extremum M, dirigatur. </s>
            <s xml:id="echoid-s3700" xml:space="preserve">Quara-
              <lb/>
            tione ſemper vmbra verſa BC, abſcindetur. </s>
            <s xml:id="echoid-s3701" xml:space="preserve">Nam ſi linea fiducię per C, tranſi-
              <lb/>
            ret, aut vmbramrectam C D, interſecaret, eſſet diſtantia vel æqualis lateri C D,
              <lb/>
            vel minor: </s>
            <s xml:id="echoid-s3702" xml:space="preserve">ac proinde dimenſione nonindigeret. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">Quoniam igitur rurſus trian-
              <lb/>
            gulum NBA, triangulo A D M, ęquiangulum eſt, propter rectos angulos B,
              <lb/>
            D, & </s>
            <s xml:id="echoid-s3704" xml:space="preserve">alternos æquales BAN, AMD; </s>
            <s xml:id="echoid-s3705" xml:space="preserve"> Si fiat,</s>
          </p>
          <note symbol="d" position="right" xml:space="preserve">29. primi.</note>
          <note symbol="e" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt part{es} vmbræ \\ verſæ BN, # ad lat{us} quadrati \\ AB, 1000. # Ita lat{us} quadrati \\ AD, 1000. # ad DM, diſtan- \\ tiam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3706" xml:space="preserve">cognita erit diſtantia DM, in partibus milleſimis Iateris quadrati AD.</s>
            <s xml:id="echoid-s3707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3708" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">
              <emph style="sc">Solent</emph>
            nonnulli Scriptores non inquirere diſtantiam propoſitam in
              <lb/>
            partibus altitudinis aſſumptę AE, vel in partibus milleſimis lateris quadrati AD;
              <lb/>
            </s>
            <s xml:id="echoid-s3710" xml:space="preserve">ſed ſolum inueſtigant, quoties altitudo electa AE, vellatus quadrati AD, in di-
              <lb/>
            ſtantia propoſita contineatur: </s>
            <s xml:id="echoid-s3711" xml:space="preserve">quod idem eſt, ac ſi altitudo, autlatus vmbræ
              <lb/>
            ſtatuatur 1. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s3713" xml:space="preserve">ita diuidunt vel partes vmbrę rectę abſciſſas per totum latus
              <lb/>
            partium 1000. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">vel totum latus vmbræ verſæ per partes vmbrę verſę abſciſlas. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">
              <lb/>
            Nam Quotiens numerus indicat, quoties altitudo A C, vel latus Quadrati in
              <lb/>
            propoſita diſtantia comprehendatur: </s>
            <s xml:id="echoid-s3716" xml:space="preserve">cum ſit,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt totum lat{us} A D, \\ partium 1000. # ad part{es} vmbræ \\ rectæ D I, # ita altitudo A E, vel la- \\ t{us} A D, vt 1. # ad diſtantiam \\ E G, vel D I.
            <lb/>
          </note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          #### Item.
            <lb/>
          Vt part{es} vmbræ ver- \\ ſæ B N, # ad totum lat{us} AB, \\ 1000. # Ita altitudo A E, vel \\ lat{us} AD, vt 1. # ad diſtantiam \\ EF, vel DM,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3717" xml:space="preserve">Hinc enim fit, vt cum ſecundum pręceptum regulę trium tertius numerus in ſe-
              <lb/>
            cundum ſit ducendus, productuſq; </s>
            <s xml:id="echoid-s3718" xml:space="preserve">numerus per primum diuidendus, ſatis ſit,
              <lb/>
            ſi ſecundus per primum diuidatur: </s>
            <s xml:id="echoid-s3719" xml:space="preserve">quando quidem vnitas in tertio loco poſita,
              <lb/>
            ſi multiplicet ſecundum numerum, eundem ſecundum numerum procreat, &</s>
            <s xml:id="echoid-s3720" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3722" xml:space="preserve">
              <emph style="sc">Hac</emph>
            ratione, ſi duæ paites milleſimę abſcindantur ex vmbra verſa, </s>
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